Shuxue Liu

Modified eigenfunction expansion methods for interaction of water waves with a semi-infinite elastic plate

Abstract The eigenfunction expansion method (will be referred to as error function method in this paper) of analysing reflection and transmission of ocean waves at a semi-infinite thin elastic plate [J Geophys Res 95 (1990) 11629; Phil Trans R Soc Lond A 347 (1994) 185] is modified and extended to cases with simply supported and built-in edges. The form of the error function in the eigenfunction expansion method of Fox and Squire [J Geophys Res 95 (1990) 11629] has been modified based on a dimensional analysis and also extended to plates with either a simply supported or a built-in edge. The modified error function does not include the so-called Lagrange multipliers used in the original method and therefore the modified solution is independent of the selection of the Lagrange multipliers. It is demonstrated that the modified error function method satisfies the relation of energy conservation very well for the three edge conditions examined. The relation of energy conservation for plates is derived for elastic plates with simply supported and built-in edges and it is found that the relation of energy conservation for a free edge is also held for simply supported and built-in edges. In addition, a minor modification has also been made to the eigenfunction method (will be called inner product method in this study) of Sahoo et al. [Proceedings of 10th International Offshore and Polar Engineering Conference 3 (2000) 594]. It will be shown that the modified inner product method becomes mathematically well defined. The modified coefficient matrixes for different edge conditions are diagonal and thus the linear simultaneous equations can be solved very easily. It is also demonstrated with examples that the extended error function method and the modified inner product method give identical results.

Refraction and diffraction of random waves through breakwater

A physical model study of combined refraction and diffraction of waves through a breakwater gap at different incident angles was conducted. Both regular and random waves with narrow and broad frequency and direction spreading were studied. Besides the presence of a mild bottom slope in the lee of the breakwater, the distribution of wave heights across the width of a navigation channel inside the model harbor was also simulated. In addition to contributing to an understanding of the phenomenon of refraction and diffraction of random waves, the relatively complete set of data obtained can serve as a benchmark for testing of numerical models.

Laboratory Study of Unidirectional Focusing Waves in Intermediate Depth Water

The results of laboratory measurements of large focusing wave groups, which were generated using the New Wave theory, are presented. The influences of both the steepness and frequency bandwidth on focused wave characteristics were examined. The influence of frequency bandwidth on focused wave groups with small and moderate steepness was very small. However, for cases with the large steepness, the nonlinearity increased with increasing bandwidth frequency and widened free-wave regimes are identified for those cases with large steepness at the focal location. The underlying nonlinear phase coupling of focused waves was examined using wavelet-based bicoherence and biphase, which can detect nonlinear phase coupling in a short time series. For wave groups with large initial steepness, as wave groups approached the focal location, the values of bicoherence between primary waves and its higher harmonics progressively increased to 1 and the corresponding biphase was gradually close to zero, suggesting that an extreme wave event can be produced by considering Stokes-like nonlinearity to very high-order. Furthermore, the fast change of bicoherence of focused wave groups indicates that the nonlinear energy transfer within focusing waves is faster than that of nonfocusing wave trains.

Numerical investigation of multidirectional random wave interaction with a large cylinder

To investigate the multidirectional wave run-up and forces on a large cylinder, a numerical model of multidirectional random wave loads on a large-scale cylinder is established based on the linear theory of wave interaction with a large-scale bottom-mounted vertical cylinder. The incident directional wave is specified using a discrete form of the Mitsuyasu-type spreading function. A wave basin experiment was carried out, and the numerical calculation results were verified by the results of the physical experiment. The results indicate that the wave directionality has significant effects on the distribution of the wave run-up around the cylinder. The transverse wave force occurs due to which the multidirectional waves at the two sides of the cylinder are totally different from each other at any time because of the wave directionality. Specially, for the multidirectional random wave with small directional spreading parameter (su2009=u20095), the transverse force Fy is about 57% of the normal force Fx and cannot be neglected any more. Results can provide reference for the real engineering design.